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    <meta name="description" content="问题回顾 亚马逊在其创建的在线市场中，为顾客提供了对购买进行评分和评价的机会。个人评级（称为“星级”）使购买者可以使用 1（低评级，低满意度）到 5（高评级，高满意度）的等级来表示他们对产品的满意度。此外，客户可以提交文本消息（称为“评论”），以表达有关产品的更多意见和信息。其他客户可以在这些评论中提交有帮助或无帮助的评级（称为“帮助评级”），以协助他们自己的产品购买决策。公司使用这些数据来深入">
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<meta property="og:description" content="问题回顾 亚马逊在其创建的在线市场中，为顾客提供了对购买进行评分和评价的机会。个人评级（称为“星级”）使购买者可以使用 1（低评级，低满意度）到 5（高评级，高满意度）的等级来表示他们对产品的满意度。此外，客户可以提交文本消息（称为“评论”），以表达有关产品的更多意见和信息。其他客户可以在这些评论中提交有帮助或无帮助的评级（称为“帮助评级”），以协助他们自己的产品购买决策。公司使用这些数据来深入">
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        <h2 id="问题回顾"><a class="markdownIt-Anchor" href="#问题回顾"></a> 问题回顾</h2>
<p>亚马逊在其创建的在线市场中，为顾客提供了对购买进行评分和评价的机会。个人评级（称为“星级”）使购买者可以使用 1（低评级，低满意度）到 5（高评级，高满意度）的等级来表示他们对产品的满意度。此外，客户可以提交文本消息（称为“评论”），以表达有关产品的更多意见和信息。其他客户可以在这些评论中提交有帮助或无帮助的评级（称为“帮助评级”），以协助他们自己的产品购买决策。公司使用这些数据来深入了解客户参与的市场，参与的时间以及产品设计功能选择的潜在成功。</p>
<p>阳光公司计划在网络上推出和销售三种新产品：微波炉、婴儿奶嘴和吹风机。他们已聘请您的团队作为顾问，识别与其他竞争产品相关的客户提供的过去评级和评论中的关键模式、关系、度量和参数，用于 1）告知其在线销售策略；2）识别潜在的重要设计功能，提高产品的吸引力。阳光公司过去曾使用数据为销售策略提供信息，但他们以前从未使用过这种特殊的组合和数据类型。阳光公司特别感兴趣的是这些数据中的基于时间的模式，以及顾客的互动方式是否有助于公司打造成功的产品。</p>
<p>为了帮助您，阳光公司的数据中心为您提供了该项目的三个数据文件：hair_dryer.tsv，microwave.tsv 和 pacifier.tsv。这些数据代表在数据指示的时间段内在亚马逊市场上出售的微波炉、婴儿奶嘴和吹风机的客户提供的评级和评论。并且，这里还提供了数据标签定义的词汇表，提供的数据文件包含您应用于此问题的唯一数据。</p>
<p>要求:</p>
<p>1.分析提供的三个产品数据集，以使用数学证据来识别、描述和支持有意义的定量和/或定性模式、关系、量度和参数，这些数据在星级、评论和帮助评分之内和之间进行，这将有助于阳光公司在他们三个新的在线市场产品中都取得成功。</p>
<p>2.使用您的分析来解决阳光公司市场总监的以下特定问题和要求：</p>
<ul>
<li>一旦阳光公司的三款产品在网络市场上销售，根据对其<strong>信息量最大</strong>的评级和评论确定数据衡量标准。</li>
<li>在每个数据集中识别并讨论基于时间的度量和模式，这些度量和模式可能表明产品在网络市场中的声誉在上升或下降。</li>
<li>确定最能表明潜在成功或失败产品的基于文本的度量和基于评级的度量的组合。</li>
<li>特定星级会引起更多评论吗？例如，在看到一系列低星级评级之后，客户是否更有可能撰写某种类型的评论？<br />
诸如“热情”，“失望”之类的基于文本的评论的特定质量描述符是否与评级水平密切相关。</li>
</ul>
<p><a href="https://mp.weixin.qq.com/s/R4Qs0xAsT1YvXBujyTYv7Q" target="_blank" rel="noopener">具体题目点击这里</a></p>
<h2 id="基于评星与评论的衡量标准"><a class="markdownIt-Anchor" href="#基于评星与评论的衡量标准"></a> 基于评星与评论的衡量标准</h2>
<p>按照题目的要求，对于评论的情感分析是必要的，并且要设计一个结合评分与评论的衡量标准，这个衡量标准可以帮助公司追踪产品在市面上的情况。还要求<strong>信息量最大(most informative)</strong>，这是一个很奇怪的要求。我们看看针对这个问题各个队伍是怎么做的：</p>
<h3 id="team-2002116"><a class="markdownIt-Anchor" href="#team-2002116"></a> Team 2002116</h3>
<p>(该团队似乎没有做第一问，但不重要)</p>
<p>该团队提出了<strong>重要程度(importance)<strong>来评价评论与星级的信息量。对于评论，提出CE-VARDE模型用于对其进行情感分析，将评论的情感分为五类，发现每一条评价与其对应的评分（五星评分）有很强的相关性。于是该队提出的这个</strong>重要程度</strong>指标将是一个结合了文本，评星之间的真实度，相关性的指标（fidelity, correlation）。</p>
<p>评星的处理：首先该队分析了对于每一个产品不同评星的占比。其次该队将评星表示为矢量形式，这是该队在评星上做的很重要的操作。得到的VEC编码是概率向量，</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mtext mathvariant="bold">VEC(s)</mtext><mo>=</mo><mo stretchy="false">(</mo><mi>v</mi><mi>e</mi><msubsup><mi>c</mi><mi>s</mi><mn>1</mn></msubsup><mo separator="true">,</mo><mi>v</mi><mi>e</mi><msubsup><mi>c</mi><mi>s</mi><mn>2</mn></msubsup><mo separator="true">,</mo><mi>v</mi><mi>e</mi><msubsup><mi>c</mi><mi>s</mi><mn>3</mn></msubsup><mo separator="true">,</mo><mi>v</mi><mi>e</mi><msubsup><mi>c</mi><mi>s</mi><mn>4</mn></msubsup><mo separator="true">,</mo><mi>v</mi><mi>e</mi><msubsup><mi>c</mi><mi>s</mi><mn>5</mn></msubsup><msup><mo stretchy="false">)</mo><mi>T</mi></msup><mo separator="true">,</mo><mi>s</mi><mo>∈</mo><mo stretchy="false">{</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mn>4</mn><mo separator="true">,</mo><mn>5</mn><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\textbf{VEC(s)}=(vec_s^1,vec_s^2,vec_s^3,vec_s^4,vec_s^5)^T ,s\in \{1,2,3,4,5\} 
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord text"><span class="mord textbf">VEC(s)</span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.1413309999999999em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="mord mathdefault">e</span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em;"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">s</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="mord mathdefault">e</span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em;"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">s</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="mord mathdefault">e</span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em;"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">s</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="mord mathdefault">e</span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em;"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">s</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="mord mathdefault">e</span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em;"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">s</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913309999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">s</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">4</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">5</span><span class="mclose">}</span></span></span></span></span></p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>v</mi><mi>e</mi><msubsup><mi>c</mi><mi>s</mi><mi>i</mi></msubsup><mo>=</mo><mfrac><msup><mi>e</mi><mfrac><msup><mrow><mo fence="true">∣</mo><mi>i</mi><mo>−</mo><mi>s</mi><mo fence="true">∣</mo></mrow><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>σ</mi><mn>0</mn></msub></mrow></mfrac></msup><mrow><munderover><mo>∑</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mn>5</mn></munderover><msup><mi>e</mi><mfrac><msup><mrow><mo fence="true">∣</mo><mi>j</mi><mo>−</mo><mi>s</mi><mo fence="true">∣</mo></mrow><mn>2</mn></msup><mrow><mn>2</mn><msub><mi>σ</mi><mn>0</mn></msub></mrow></mfrac></msup></mrow></mfrac></mrow><annotation encoding="application/x-tex">vec_s^i=\frac{e^{\frac{\left | i-s \right |^2}{2\sigma _0}}}{\sum _{j=1}^5e^{\frac{\left | j-s \right |^2}{2\sigma _0}}} 
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.121664em;vertical-align:-0.247em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="mord mathdefault">e</span><span class="mord"><span class="mord mathdefault">c</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8746639999999999em;"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">s</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.6958980000000006em;vertical-align:-1.644858em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.0510400000000004em;"><span style="top:-2.165em;"><span class="pstrut" style="height:3.37404em;"></span><span class="mord"><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.954008em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.43581800000000004em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.31904em;"><span style="top:-3.4983700000000004em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1723857142857144em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3447999999999998em;margin-left:-0.03588em;margin-right:0.1em;"><span class="pstrut" style="height:2.64444em;"></span><span class="mord mtight">0</span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29964em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.2255000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.5020714285714285em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="minner mtight"><span class="minner mtight"><span class="mopen mtight delimcenter" style="top:0em;"><span class="mtight">∣</span></span><span class="mord mathdefault mtight" style="margin-right:0.05724em;">j</span><span class="mbin mtight">−</span><span class="mord mathdefault mtight">s</span><span class="mclose mtight delimcenter" style="top:0em;"><span class="mtight">∣</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9384399999999999em;"><span style="top:-2.93844em;margin-right:0.1em;"><span class="pstrut" style="height:2.64444em;"></span><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5580285714285714em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.60404em;"><span class="pstrut" style="height:3.37404em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-4.05104em;"><span class="pstrut" style="height:3.37404em;"></span><span class="mord"><span class="mord"><span class="mord mathdefault">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.3740400000000002em;"><span style="top:-3.4983700000000004em;margin-right:0.05em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mopen nulldelimiter sizing reset-size3 size6"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.250957142857143em;"><span style="top:-2.656em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3447999999999998em;margin-left:-0.03588em;margin-right:0.1em;"><span class="pstrut" style="height:2.64444em;"></span><span class="mord mtight">0</span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29964em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.2255000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line mtight" style="border-bottom-width:0.049em;"></span></span><span style="top:-3.5020714285714285em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="minner mtight"><span class="minner mtight"><span class="mopen mtight delimcenter" style="top:0em;"><span class="mtight">∣</span></span><span class="mord mathdefault mtight">i</span><span class="mbin mtight">−</span><span class="mord mathdefault mtight">s</span><span class="mclose mtight delimcenter" style="top:0em;"><span class="mtight">∣</span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.04844em;"><span style="top:-3.04844em;margin-right:0.1em;"><span class="pstrut" style="height:2.64444em;"></span><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.5580285714285714em;"><span></span></span></span></span></span><span class="mclose nulldelimiter sizing reset-size3 size6"></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.644858em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p>观察上式，VEC(s)可以看做是以S为均值的正态分布的离散取值，表示对于一个S星产品分别取1,2,3,4,5星的概率。<strong>这种硬变软，类似硬聚类到软聚类的数据处理方法是可以借鉴的。</strong></p>
<p>Contextual Entropy VADER（CE-VADER混合模型）进行的情感分析：本团队对评论做情感分析用到了两个模型，CE[<a href="https://www.researchgate.net/publication/271882500_Using_a_contextual_entropy_model_to_expand_emotion_words_and_their_intensity_for_the_sentiment_classification_of_stock_market_news" target="_blank" rel="noopener">LINK</a>]与VADER[<a href="https://ojs.aaai.org/index.php/ICWSM/article/view/14550" target="_blank" rel="noopener">LINK</a>]，相关论文见链接。</p>
<p>CE过程：80%做训练，20%做测试，将训练集中的句子分解成单词，其中统计出它们的频率。高频的情感词被挑出作为种子词，由我们手动标注，而低频的则被舍弃。词被标注为五类情感。在CE的模型设定中衡量一则评论中两个单词的距离也用到了类似正态分布度量的exp(),可以看做是一种距离的度量模式，因为具有非线性满足了该团队要求的“距离越近其权重越大”的特点。该团队用了KL散度衡量上文向量与下文向量之间的距离，同时考虑到KL散度的非对称，对其进行修改得到了满足对称的新的距离度量模式，简单的来说就是将正向和逆向的距离相加和。</p>
<p>另，该团队用$ S(a,b)=\frac{1}{1+D(a,b)} $来进行距离与相似度的转换，我之前在做类似问题的时候是用对数函数，两者在曲线形式上是一致的,观察图像可以知道用1/x形式转换的距离更加的稀疏，更加的远。</p>
<p>CE与VADER的结合，用参数<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault">λ</span></span></span></span>确定两种的占比，该队伍在这里用融合系数fused coefficient称呼它，可以借鉴。再使用softmax回归，在这里被称为smoothing function，于是这样将情感的得分也压缩到了0-1之间，与之前对评星的处理达到了一致（区间缩放）。</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>I</mi><mi>N</mi><mi>T</mi><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">)</mo><mo>=</mo><mi>s</mi><mi>o</mi><mi>f</mi><mi>t</mi><mi>m</mi><mi>a</mi><mi>x</mi><mo stretchy="false">(</mo><mi>λ</mi><mi>C</mi><mi>E</mi><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>λ</mi><mo stretchy="false">)</mo><mi>V</mi><mi>A</mi><mi>D</mi><mi>E</mi><mi>R</mi><mo stretchy="false">(</mo><mi>R</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">INT(R)=softmax(\lambda CE(R)+(1-\lambda)VADER(R)) 
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">I</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">s</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mord mathdefault">t</span><span class="mord mathdefault">m</span><span class="mord mathdefault">a</span><span class="mord mathdefault">x</span><span class="mopen">(</span><span class="mord mathdefault">λ</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord mathdefault" style="margin-right:0.05764em;">E</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">λ</span><span class="mclose">)</span><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="mord mathdefault">A</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mord mathdefault" style="margin-right:0.05764em;">E</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mclose">)</span><span class="mclose">)</span></span></span></span></span></p>
<p>一组描述了某一对象的元组在数学中如何表述，例如obj_1=(feature1,feature2,feature3)，在集合论中被称为ordered pair，有序对，在论文中可以借鉴这种写法。</p>
<p>评星如何与评论结合，这涉及到<strong>多个指标如何确定到一个综合指标</strong>，是简单的相加吗？看看该团队如何处理</p>
<p>定义综合性指标importance IMP:</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>I</mi><mi>M</mi><mi>P</mi><mo stretchy="false">(</mo><mi>i</mi><mi>d</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mi>h</mi><msub><mi>v</mi><mrow><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">)</mo><mo>⋅</mo><mi>e</mi><mi>x</mi><mi>p</mi><mo stretchy="false">[</mo><mo>−</mo><mi>α</mi><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mfrac><mrow><mi>I</mi><mi>N</mi><mi>T</mi><mo stretchy="false">(</mo><msub><mi>R</mi><mrow><mi>i</mi><mi>d</mi></mrow></msub><mo>⋅</mo><mi>V</mi><mi>E</mi><mi>C</mi><mo stretchy="false">(</mo><msub><mi>s</mi><mrow><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><mrow><mrow><mo fence="true">∥</mo><mi>I</mi><mi>N</mi><mi>T</mi><mo stretchy="false">(</mo><msub><mi>R</mi><mrow><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">)</mo><mo fence="true">∥</mo></mrow><mrow><mo fence="true">∥</mo><mi>V</mi><mi>E</mi><mi>C</mi><mo stretchy="false">(</mo><msub><mi>s</mi><mi>i</mi></msub><mi>d</mi><mo stretchy="false">)</mo><mo fence="true">∥</mo></mrow></mrow></mfrac><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mo>⋅</mo><mo stretchy="false">[</mo><mi>β</mi><mo stretchy="false">(</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>5</mn></munderover><mi>i</mi><mi>n</mi><msubsup><mi>t</mi><mi>R</mi><mi>i</mi></msubsup><mi>l</mi><mi>o</mi><mi>g</mi><mo stretchy="false">(</mo><mi>i</mi><mi>n</mi><msubsup><mi>t</mi><mi>R</mi><mi>i</mi></msubsup><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">IMP(id)=(1+hv_{id})\cdot exp[-\alpha (1-\frac{INT(R_{id}\cdot VEC(s_{id}))}{\left \| INT(R_{id}) \right \|\left \| VEC(s_id) \right \|})]\cdot [\beta (\sum _{i=1}^5int^i_Rlog(int^i_R))] 
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">I</span><span class="mord mathdefault" style="margin-right:0.10903em;">M</span><span class="mord mathdefault" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathdefault">i</span><span class="mord mathdefault">d</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">h</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">e</span><span class="mord mathdefault">x</span><span class="mord mathdefault">p</span><span class="mopen">[</span><span class="mord">−</span><span class="mord mathdefault" style="margin-right:0.0037em;">α</span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="minner"><span class="mopen delimcenter" style="top:0em;">∥</span><span class="mord mathdefault" style="margin-right:0.07847em;">I</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mclose delimcenter" style="top:0em;">∥</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">∥</span><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="mord mathdefault" style="margin-right:0.05764em;">E</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathdefault">d</span><span class="mclose">)</span><span class="mclose delimcenter" style="top:0em;">∥</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.07847em;">I</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:-0.00773em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="mord mathdefault" style="margin-right:0.05764em;">E</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose">)</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:3.0787820000000004em;vertical-align:-1.277669em;"></span><span class="mopen">[</span><span class="mord mathdefault" style="margin-right:0.05278em;">β</span><span class="mopen">(</span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8011130000000004em;"><span style="top:-1.872331em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.277669em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">i</span><span class="mord mathdefault">n</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8746639999999999em;"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.00773em;">R</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord mathdefault">i</span><span class="mord mathdefault">n</span><span class="mord"><span class="mord mathdefault">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8746639999999999em;"><span style="top:-2.4530000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.00773em;">R</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mclose">)</span><span class="mclose">]</span></span></span></span></span></p>
<p>分析这个公式，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>I</mi><mi>N</mi><mi>T</mi></mrow><annotation encoding="application/x-tex">INT</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">I</span><span class="mord mathdefault" style="margin-right:0.10903em;">N</span><span class="mord mathdefault" style="margin-right:0.13889em;">T</span></span></span></span>情感得分，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>V</mi><mi>E</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">VEC</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="mord mathdefault" style="margin-right:0.05764em;">E</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span></span></span></span>评星的向量编码，都是正态分布的离散化形式，<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn><mo>−</mo><mfrac><mrow><mi>I</mi><mi>N</mi><mi>T</mi><mo stretchy="false">(</mo><msub><mi>R</mi><mrow><mi>i</mi><mi>d</mi></mrow></msub><mo>⋅</mo><mi>V</mi><mi>E</mi><mi>C</mi><mo stretchy="false">(</mo><msub><mi>s</mi><mrow><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><mrow><mrow><mo fence="true">∥</mo><mi>I</mi><mi>N</mi><mi>T</mi><mo stretchy="false">(</mo><msub><mi>R</mi><mrow><mi>i</mi><mi>d</mi></mrow></msub><mo stretchy="false">)</mo><mo fence="true">∥</mo></mrow><mrow><mo fence="true">∥</mo><mi>V</mi><mi>E</mi><mi>C</mi><mo stretchy="false">(</mo><msub><mi>s</mi><mi>i</mi></msub><mi>d</mi><mo stretchy="false">)</mo><mo fence="true">∥</mo></mrow></mrow></mfrac></mrow><annotation encoding="application/x-tex">1-\frac{INT(R_{id}\cdot VEC(s_{id}))}{\left \| INT(R_{id}) \right \|\left \| VEC(s_id) \right \|}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.53em;vertical-align:-0.52em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.01em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="minner mtight"><span class="mopen mtight delimcenter" style="top:0em;"><span class="mtight">∥</span></span><span class="mord mathdefault mtight" style="margin-right:0.07847em;">I</span><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="mopen mtight">(</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-left:-0.00773em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span><span class="mclose mtight">)</span><span class="mclose mtight delimcenter" style="top:0em;"><span class="mtight">∥</span></span></span><span class="minner mtight"><span class="mopen mtight delimcenter" style="top:0em;"><span class="mtight">∥</span></span><span class="mord mathdefault mtight" style="margin-right:0.22222em;">V</span><span class="mord mathdefault mtight" style="margin-right:0.05764em;">E</span><span class="mord mathdefault mtight" style="margin-right:0.07153em;">C</span><span class="mopen mtight">(</span><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathdefault mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mord mathdefault mtight">d</span><span class="mclose mtight">)</span><span class="mclose mtight delimcenter" style="top:0em;"><span class="mtight">∥</span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.485em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.07847em;">I</span><span class="mord mathdefault mtight" style="margin-right:0.10903em;">N</span><span class="mord mathdefault mtight" style="margin-right:0.13889em;">T</span><span class="mopen mtight">(</span><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-left:-0.00773em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span><span class="mbin mtight">⋅</span><span class="mord mathdefault mtight" style="margin-right:0.22222em;">V</span><span class="mord mathdefault mtight" style="margin-right:0.05764em;">E</span><span class="mord mathdefault mtight" style="margin-right:0.07153em;">C</span><span class="mopen mtight">(</span><span class="mord mtight"><span class="mord mathdefault mtight">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mord mathdefault mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span><span class="mclose mtight">)</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>是衡量这两个向量之间的余弦距离(1减余弦相似度)，余弦距离常见于NLP任务中衡量两个词向量的相似度。<strong>相比欧氏距离，余弦距离更加注重两个向量在方向上的差异。</strong></p>
<p>$- \sum _{i=1}<sup>5int</sup>i_Rlog(int^i_R) $表示该评论的熵。</p>
<p>另附余弦相似度的一个常用操作，数值在整体上减去均值，见<a href="https://blog.csdn.net/liunian920305/article/details/73456736" target="_blank" rel="noopener">[链接]</a></p>
<p>总结：团队围绕着如何确定一条评论的重要性开展研究，从一条评论最显著的两个方面评星、评论文本分别入手，如果评星与评论呈现强关联（即文章中的余弦相似度高）则认为它是好的评论的一个部分因素，另外两条因素为帮助度，评论情感得分的熵。其中向量化的处理以及转换成概率模型是很值得借鉴的。</p>
<h3 id="team-2003717"><a class="markdownIt-Anchor" href="#team-2003717"></a> Team 2003717</h3>
<p>该团队第一问采用LDA Topic model对文本进行了简单分析。LDA Topic model的相关内容见<a href="https://github.com/NLP-LOVE/ML-NLP/tree/master/Machine%20Learning/5.3%20Topic%20Model" target="_blank" rel="noopener">[链接]</a>。这个LDA跟线性判别那个LDA没有关系。一个是Latent Dirichlet Allocation隐含狄利克雷分布，Linear Discriminant Analysis线性判别分析。其余指标也进行了基本的分析。</p>
<p>在处理完数据的基础上，针对第二问第一题，该团队设计了三种基于评级和评论的数据度量模式</p>
<p>1.加权评星比率，写的很怪，我看不懂这个定义过程。按照论文的描述应当是将对应评星的帮助度作为权重来修正实际上的评星。</p>
<p>2.加权评论情感得分的均值与标准差。这个团队在情感分析的时候没有采用NLP的主流情感分析工具而是采用了自己的一套逻辑。但是还是看不懂，前面定义了词集$\omega $但是接下来都没有用过，以及很多符号看不懂含义，决定放弃阅读，不浪费时间。</p>
<p>3.评论中的产品属性。利用LDA Topic model分析了评论中所描述的对应产品的多个属性，并根据各种属性出现的次数建立模型。</p>
<h3 id="team-2004647"><a class="markdownIt-Anchor" href="#team-2004647"></a> Team 2004647</h3>
<p>该团队对于评星与评论的综合用了自己提出的RRBS模型，其结果为一个score，并且包含了时间维度:</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>s</mi><mi>c</mi><mi>o</mi><mi>r</mi><msubsup><mi>e</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>k</mi></mrow><mrow><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></msubsup><mo>=</mo><msup><mi>α</mi><mrow><mo>∘</mo><mi>λ</mi></mrow></msup><mi>β</mi></mrow><annotation encoding="application/x-tex">score_{i,k}^{(t)}=\alpha ^{\circ \lambda}\beta 
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.4822159999999998em;vertical-align:-0.4374159999999999em;"></span><span class="mord mathdefault">s</span><span class="mord mathdefault">c</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord"><span class="mord mathdefault">e</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0448em;"><span style="top:-2.3986920000000005em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span></span></span></span><span style="top:-3.2198em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathdefault mtight">t</span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4374159999999999em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.093548em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.0037em;">α</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∘</span><span class="mord mathdefault mtight">λ</span></span></span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.05278em;">β</span></span></span></span></span></p>
<p>i为产品类型，k表示第k种产品，t是以月为单位的时间尺度，$ \lambda <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">是</mi><mi mathvariant="normal">权</mi><mi mathvariant="normal">重</mi><mi mathvariant="normal">，</mi></mrow><annotation encoding="application/x-tex">是权重，</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0em;vertical-align:0em;"></span><span class="mord cjk_fallback">是</span><span class="mord cjk_fallback">权</span><span class="mord cjk_fallback">重</span><span class="mord cjk_fallback">，</span></span></span></span> \alpha <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">是</mi><mi mathvariant="normal">一</mi><mi mathvariant="normal">个</mi><mi>n</mi><mi mathvariant="normal">维</mi><mi mathvariant="normal">行</mi><mi mathvariant="normal">向</mi><mi mathvariant="normal">量</mi><mi mathvariant="normal">，</mi><mi mathvariant="normal">以</mi><mi mathvariant="normal">一</mi><mi mathvariant="normal">个</mi><mi mathvariant="normal">月</mi><mi mathvariant="normal">为</mi><mi mathvariant="normal">一</mi><mi mathvariant="normal">组</mi><mi mathvariant="normal">，</mi><mi>n</mi><mi mathvariant="normal">表</mi><mi mathvariant="normal">示</mi><mi mathvariant="normal">一</mi><mi mathvariant="normal">个</mi><mi mathvariant="normal">月</mi><mi mathvariant="normal">的</mi><mi mathvariant="normal">评</mi><mi mathvariant="normal">论</mi><mi mathvariant="normal">数</mi><mi mathvariant="normal">。</mi></mrow><annotation encoding="application/x-tex">是一个n维行向量，以一个月为一组，n表示一个月的评论数。</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord cjk_fallback">是</span><span class="mord cjk_fallback">一</span><span class="mord cjk_fallback">个</span><span class="mord mathdefault">n</span><span class="mord cjk_fallback">维</span><span class="mord cjk_fallback">行</span><span class="mord cjk_fallback">向</span><span class="mord cjk_fallback">量</span><span class="mord cjk_fallback">，</span><span class="mord cjk_fallback">以</span><span class="mord cjk_fallback">一</span><span class="mord cjk_fallback">个</span><span class="mord cjk_fallback">月</span><span class="mord cjk_fallback">为</span><span class="mord cjk_fallback">一</span><span class="mord cjk_fallback">组</span><span class="mord cjk_fallback">，</span><span class="mord mathdefault">n</span><span class="mord cjk_fallback">表</span><span class="mord cjk_fallback">示</span><span class="mord cjk_fallback">一</span><span class="mord cjk_fallback">个</span><span class="mord cjk_fallback">月</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">评</span><span class="mord cjk_fallback">论</span><span class="mord cjk_fallback">数</span><span class="mord cjk_fallback">。</span></span></span></span>\beta$则是n维列向量，其定义如下：</p>
<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>β</mi><mo>=</mo><mi>A</mi><mi mathvariant="normal">Φ</mi></mrow><annotation encoding="application/x-tex">\beta =A\Phi  
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.05278em;">β</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault">A</span><span class="mord">Φ</span></span></span></span></span></p>
<p>A是一个n*n矩阵用来描述评论的情感强度,<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Φ</mi></mrow><annotation encoding="application/x-tex">\Phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Φ</span></span></span></span>n维列向量，用来量化评论的语义信息和其他影响属性。接下来根据数据的方方面面定义<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Φ</mi></mrow><annotation encoding="application/x-tex">\Phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Φ</span></span></span></span>中元素的数值。情感的得分用到了Afinn库。</p>
<p>如果抽象到思维层面，就是：<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">总</mi><mi mathvariant="normal">得</mi><mi mathvariant="normal">分</mi><mo>=</mo><mi mathvariant="normal">评</mi><msup><mi mathvariant="normal">星</mi><mi>λ</mi></msup><mo>⋅</mo><mi mathvariant="normal">评</mi><mi mathvariant="normal">论</mi><mi mathvariant="normal">得</mi><mi mathvariant="normal">分</mi></mrow><annotation encoding="application/x-tex">总得分=评星^\lambda\cdot 评论得分</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mord cjk_fallback">总</span><span class="mord cjk_fallback">得</span><span class="mord cjk_fallback">分</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.849108em;vertical-align:0em;"></span><span class="mord cjk_fallback">评</span><span class="mord"><span class="mord cjk_fallback">星</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">λ</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0em;vertical-align:0em;"></span><span class="mord cjk_fallback">评</span><span class="mord cjk_fallback">论</span><span class="mord cjk_fallback">得</span><span class="mord cjk_fallback">分</span></span></span></span>,<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">评</mi><mi mathvariant="normal">论</mi><mi mathvariant="normal">得</mi><mi mathvariant="normal">分</mi><mo>=</mo><mi mathvariant="normal">评</mi><mi mathvariant="normal">论</mi><mi mathvariant="normal">情</mi><mi mathvariant="normal">感</mi><mo>⋅</mo><mi mathvariant="normal">评</mi><mi mathvariant="normal">论</mi><mi mathvariant="normal">的</mi><mi mathvariant="normal">其</mi><mi mathvariant="normal">他</mi><mi mathvariant="normal">因</mi><mi mathvariant="normal">素</mi><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">情</mi><mi mathvariant="normal">感</mi><mi mathvariant="normal">得</mi><mi mathvariant="normal">分</mi><mi mathvariant="normal">矩</mi><mi mathvariant="normal">阵</mi><mi mathvariant="normal">的</mi><mi mathvariant="normal">主</mi><mi mathvariant="normal">对</mi><mi mathvariant="normal">角</mi><mi mathvariant="normal">线</mi><mi mathvariant="normal">元</mi><mi mathvariant="normal">素</mi><mo stretchy="false">)</mo><mo>⋅</mo><mo stretchy="false">(</mo><mi>v</mi><mi>i</mi><mi>n</mi><mi>e</mi><mi mathvariant="normal">用</mi><mi mathvariant="normal">户</mi><mo>∗</mo><mi mathvariant="normal">帮</mi><mi mathvariant="normal">助</mi><mi mathvariant="normal">度</mi><mo>∗</mo><mo>∗</mo><mi mathvariant="normal">评</mi><mi mathvariant="normal">论</mi><mi mathvariant="normal">长</mi><mi mathvariant="normal">度</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">评论得分=评论情感\cdot 评论的其他因素=(情感得分矩阵的主对角线元素)\cdot (vine用户*帮助度**评论长度)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mord cjk_fallback">评</span><span class="mord cjk_fallback">论</span><span class="mord cjk_fallback">得</span><span class="mord cjk_fallback">分</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.44445em;vertical-align:0em;"></span><span class="mord cjk_fallback">评</span><span class="mord cjk_fallback">论</span><span class="mord cjk_fallback">情</span><span class="mord cjk_fallback">感</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mord cjk_fallback">评</span><span class="mord cjk_fallback">论</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">其</span><span class="mord cjk_fallback">他</span><span class="mord cjk_fallback">因</span><span class="mord cjk_fallback">素</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">情</span><span class="mord cjk_fallback">感</span><span class="mord cjk_fallback">得</span><span class="mord cjk_fallback">分</span><span class="mord cjk_fallback">矩</span><span class="mord cjk_fallback">阵</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">主</span><span class="mord cjk_fallback">对</span><span class="mord cjk_fallback">角</span><span class="mord cjk_fallback">线</span><span class="mord cjk_fallback">元</span><span class="mord cjk_fallback">素</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="mord mathdefault">i</span><span class="mord mathdefault">n</span><span class="mord mathdefault">e</span><span class="mord cjk_fallback">用</span><span class="mord cjk_fallback">户</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.46528em;vertical-align:0em;"></span><span class="mord cjk_fallback">帮</span><span class="mord cjk_fallback">助</span><span class="mord cjk_fallback">度</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">∗</span><span class="mord cjk_fallback">评</span><span class="mord cjk_fallback">论</span><span class="mord cjk_fallback">长</span><span class="mord cjk_fallback">度</span><span class="mclose">)</span></span></span></span>。</p>
<p>总结：要善用指数函数与对数函数，善用修正项。从思维到数学公式的确定。</p>
<h3 id="team-2007707"><a class="markdownIt-Anchor" href="#team-2007707"></a> Team 2007707</h3>
<p>这个团队的论文pdf居然不能提取文字，很麻烦。</p>
<h2 id="基于时间的度量"><a class="markdownIt-Anchor" href="#基于时间的度量"></a> 基于时间的度量</h2>

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            <p>原文作者：<a href="http://xiuzhedorothy.gitee.io">宇航猫休蛰</a>
            <p>原文链接：<a href="http://xiuzhedorothy.gitee.io/2020/12/21/2020-mei-sai-c-ti-lun-wen-fen-xi/">http://xiuzhedorothy.gitee.io/2020/12/21/2020-mei-sai-c-ti-lun-wen-fen-xi/</a>
            <p>发表日期：<a href="http://xiuzhedorothy.gitee.io/2020/12/21/2020-mei-sai-c-ti-lun-wen-fen-xi/">December 21st 2020, 11:14:59 am</a>
            <p>更新日期：<a href="http://xiuzhedorothy.gitee.io/2020/12/21/2020-mei-sai-c-ti-lun-wen-fen-xi/">March 30th 2021, 3:24:19 pm</a>
            <p>版权声明：本文采用<a rel="license noopener" href="http://creativecommons.org/licenses/by-nc/4.0/" target="_blank">知识共享署名-非商业性使用 4.0 国际许可协议</a>进行许可</p>
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